This isn't directly related to your comment, but it's odd to me, grammatically, that people say Uber isn't a taxi service. It's like saying Amazon isn't a retailer--certainly it's different than the pre-internet model, but fundamentally they're providing the same service as the traditional businesses.
It depends on what you mean by the term, as there are different senses of "taxi service". In many cases, the law has long differentiated (for non-flaky reasons) between taxi services and limo services[1]. A taxi service is allowed to pick up street hails (i.e. arranged on the spot, by line-of-sight), while a limo service had to be booked and paid for through a third party.
In a way, that makes regulatory sense -- there are many issues that arise with taxis (in this sense) that don't with limos -- unnamed randos getting into a stranger's car, large amounts of cash floating around, clogging up pickup points, fighting for fares, dubious upcharges. In that sense, Uber has functioned more as a limo service than a taxi service (except for this historic association between limo services and expensive cars).
OTOH, I agree that it's ridiculous for them to claim it's "not a taxi service" in the sense of "just a technology company, bro!". It's certainly a ride service of some kind, for which safety/insurance regs are applicable and reasonable (or at least, not outrageous).
(Ditto for the claim of "we just match people up!" -- they obviously are functioning more as a service provider with tight control of the product than some kind of marketplace or matchmaker.)
[1] Despite it's name, that doesn't necessarily mean "stretch limo"; it could be a sedan.
